Changing the phase angle would change the compression ratio. 180 degrees would be 0 compression, closer to 0 degrees would raise compression. The temperature ratio follows the compression ratio.

I've never built an Alpha engine, but have read a lot about them. The first Stirling engine I built was an LTD Gamma from just a picture, no plans and it ran. When I ran the dimensions thru a LTD calculator it said it should not run. When I rebuilt it after it was dropped, I changed some dimensions and balanced the pistons and crank throws. The running temperature differential changed from over 7 degrees F to just under 3 degrees F. And it now matches what the LTD calculator says. Changing the phase angle changes the RPM and the running temperature.

So if you make an Alpha: balance it and get the friction down low, you might get the running temperature down low enough to call it an LTDby playing with the phase angle.

I'm not a fan of Alphas except for high temp versions, and even then they generally use heat sources that might be better and more efficiently spent elsewhere. But that said; you can lower the peak volume ratio to where it works with lower temps, with variable volume. The weight of a few inches of water in this novelty Alpha serves the purpose, but gravity limits speed. Springs in the rods or elsewhere might work for a more useful engine.

Bumpkin, in regards to high temp engines, I find that my gamma/beta models perform poorly after running for sometime in one session due to the lack of thermal isolation in the displacer piston & cylinder between cold and the hot sides.

I presume a parallel twin cylinder Alpha engine would also suffer from the cold side getting too warm too quickly through thermal conduction. The wisdom of a V arrangement for an an alpha is very compelling. The hot and the cold Pistons are separated and the crankshaft is mechanically simple. The only drawback is that it takes up more space than a parallel Alpha engine. Also the passage between the two cylinders presumably takes more dead volume, however there's some research that suggests that there's little impact on performance from that.

Also in a V type ALPHA motor there is the advantage of a more simple crankshaft. The passage between the two cylinders can contain the regenerator.With any of my motors ALPHA, BETA, or GAMMA, if they won't run all day without over heating the cold end, it's a failure, all have succeeded so far.Ian S C